For every pair of positive integers p > q we construct a one-relator group Rp,q whose Dehn function is ≃ n2α where α = log2(2p/q). The group Rp,q has no subgroup isomorphic to a Baumslag-Solitar group BS(m, n) with m != ±n, but it is not automatic, not CAT(0), and cannot act freely on a CAT(0) cube complex. This answers a long-standing question on the automaticity of one-relator groups and gives counterexamples to a conjecture of Wise. [ABSTRACT FROM AUTHOR]
The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $ \mathfrak{g}\otimes \mathbb{C}[t,t^{-1},u\vert u^2=(t^2-b^2)(t^2-c^2)]$ [ABSTRACT FROM AUTHOR]
We construct new irreducible weight modules over quantum affine algebras of type I with all weight spaces infinite dimensional. These modules are obtained by parabolic induction from irreducible modules over the Heisenberg subalgebra. [ABSTRACT FROM AUTHOR]
INFINITE dimensional Lie algebras, SUPERALGEBRAS, LIE superalgebras, INTEGERS, ZERO (The number)
Abstract
We study codimension growth of infinite dimensional Lie superalgebras over an algebraically closed field of characteristic zero. We prove that if a Lie superalgebra L is a Grassmann envelope of a finite dimensional simple Lie algebra, then the PI-exponent of L exists and is a positive integer. [ABSTRACT FROM AUTHOR]
Published
2013
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